Solution to Bi-linear SDOF Compound Stochastic Vibration

Abstract:

Based on the research of linear SDOF compound stochastic vibration and Monte Carlo simulation,non-linear improved stochastic perturbation method is adopted to solve single stochastic problem,and bi-linear SDOF stochastic structure is expanded to mean part and variation part.Then, the probability distribution type of stochastic response is assumed as normal distribution or uniform distribution. As a result,bi-linear compound stochastic differential equation is expanded to linear perturbation stochastic differential equations.Stochastic response is obtained with the pseudo excitation method and iteration.A case study shows that the combination of non-linear improved stochastic perturbation method with pseudo excitation method can get relatively accurate result of stochastic response of non-linear compound stochastic vibration system.For more accurate results,precise pre-estimate of the probability distribution type of stochastic response is very important.